Strong relationships

Among the first numerical data analysis fruits of James Burns' archive research (see "Gunning for data", 22 February) are a set of surprisingly strong correlations between crewing levels, tonnage and gunnery on British naval ships during the Revolutionary and Napoleonic Wars period.

James comments on the correlations below, and his plots to illustrate them are reproduced here (click them for an enlarged view in a separate browser window or tab).

“The pairwise relationships between all three variables can be represented as linear, as shown in my scatter and trendline.

The plots also show that a third order polynomial (or cubic) model fits the relationship between tonnage and crew level even better. I explored other models, but found that a second order (quadratic) fit brought very little improvement, third order was the big step, and that there was no benefit from going beyond that to fourth, fifth or sixth order.

This is interesting because it means that crewing was a greater relative overhead cost of expansion in mid range vessels than in first rate ships of the line or in the smaller sloops and brigs.

Although the regression fit for gunnery power against tonnage can be slightly improved by moving to a quadratic model, the difference is not great enough (on this data set, at least) to justify the change.

The correlation of gunnery to crew is firmly linear, and shows no improvement at all if the polynomial order of the model is increased. This probably reflects the composition of fighting vessel crews of the period. There were no separate gunnery personnel, and watch rotation was suspended during military engagement, so total ship's the crew reflected the numbers required to man guns at action stations.”

Gunning for data

Sixteen year old GCSE+ student James Burns has been fascinated for years by the British navy in the late eighteenth and early nineteenth centuries CE. He has his sights set on an academic career built around his interest, and so it seemed the obvious basis for his Higher Project Qualification this year.

His chosen project title is An investigation into the relationship of equipage and materiel to ship size in British naval vessels of the Napoleonic era, with some modern comparisons, but like any enthusiast he has not limited himself strictly to it: his project submission will summarise a much larger paper (currently 5500 words and counting, with an estimated final length of 15000) to be published separately.

The work has also spawned two websites which support and document his research, of which he comments:

“I have made two trips down to Portsmouth, the home port of the royal Navy and where I’m most likely to find the sources I needed. The first, late last year, was to the Royal Armouries in Fort Nelson, on Portsdown Hill. I was looking primarily at guns; their weight, calibre etc.

My second visit, during last week's February half term, was far more interesting. I was fortunate enough to view some of the documents in the archive of the Royal Naval Museum located at the Historic Dockyards in Portsmouth (also the home of HMS Victory). There were some interesting moments when attempting to get through security, but once past that it all went incredibly smoothly. I was taken to the reading room and presented with the documents I had requested (mostly ship drafts and sail plans). Looking at the sources was fascinating and, to be honest, I feel very privileged to have been allowed to view them.

With my research complete (for now, at any rate...), all I have to do is write it up!”

James Nicholls completes HPQ design phase

James Nicholls, Sixth Form Academy student, has been working throughout this term on a Higher Project qualification based around his passion for architectural design.

Taking an assignment from his maths course as his starting point, James gathered the dimensions, textures and notes necessary to construct a detailed model of Millennium Square.

James describes the square as “a large out-door public space in the city centre. It was constructed around 1999-2000, as part of the @Bristol development of tourist attractions. The Square sits above an underground car park and includes public seating areas, water features and sculptures. One of the most striking features of the Square is the large, stainless-steel mirror sphere which houses the Planetarium.”

He also researched the software tools available to him. As he says in his working notes, “There is a wide range of CAD programs available, all with slightly different features and varying levels of functionality”. He examined the features available in a selection of these programs, finally settling on Google's SketchUp. “I have chosen to use SketchUp due to its ease of use and being available as freeware”, James comments. “Even though it's a free program, it does seem to be quite capable of producing professional-looking models, just as good as the high-end programs which can cost several thousands to purchase in full version. It runs on both MacOS and Windows, giving it a wide field of potential use.”

Starting from the basic measurements of the square and its major features, James began by constructing a skeleton representation of the space. Making repeated return visits to acquire more detailed dimensional and positional information, he then progressively refined this first model. Smaller and smaller features were added, and the representation of each aspect developed.

On each visit to the square James also used the camera in his phone to gather photographs from which he could derive visual aspects of the model – surface textures and the exact curvature of a roof line, for instance. Components within the model (such as the car park, the water features, the @Bristol building and planetarium shown here, and so on) were initially developed as separate, free standing entities, finally being brought together for integration into the whole.

As the term ends, James has unveiled his complete model complete with vegetation and a population of visitors. The image here gives a general overview from one angle, but users with access to the model itself (more than 25 megabytes of it!) and a copy of SketchUp can fly through it, look at it from any viewpoint (including a bird's eye or pedestrian's eye view, for example), zoom in to closely examine each part of it, and so on.

Click on any image to enlarge it. For more information on the Higher Project and Extended Project qualifications, contact the Sixth Form Academy.